LMFDB - Embedded newform 147.6.e.o.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 $ x^8 - x^7 + 98x^6 + 83x^5 + 9122x^4 - 91x^3 + 28567x^2 + 2058x + 86436
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.4
Root			$5.09061 - 8.81720i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.o.67.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.59061 - 7.95118i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-26.1475 - 45.2888i) q^{4} +(11.0358 - 19.1146i) q^{5} +82.6311 q^{6} -186.333 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(4.59061 - 7.95118i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-26.1475 - 45.2888i) q^{4} +(11.0358 - 19.1146i) q^{5} +82.6311 q^{6} -186.333 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-101.322 - 175.495i) q^{10} +(-208.355 - 360.881i) q^{11} +(235.327 - 407.599i) q^{12} -797.918 q^{13} +198.644 q^{15} +(-18.6623 + 32.3240i) q^{16} +(-687.775 - 1191.26i) q^{17} +(371.840 + 644.045i) q^{18} +(1156.51 - 2003.14i) q^{19} -1154.23 q^{20} -3825.91 q^{22} +(477.701 - 827.402i) q^{23} +(-838.497 - 1452.32i) q^{24} +(1318.92 + 2284.44i) q^{25} +(-3662.93 + 6344.39i) q^{26} -729.000 q^{27} -7035.29 q^{29} +(911.900 - 1579.46i) q^{30} +(630.596 + 1092.22i) q^{31} +(-2809.98 - 4867.03i) q^{32} +(1875.19 - 3247.93i) q^{33} -12629.2 q^{34} +4235.89 q^{36} +(-4888.22 + 8466.65i) q^{37} +(-10618.2 - 18391.3i) q^{38} +(-3590.63 - 6219.16i) q^{39} +(-2056.33 + 3561.67i) q^{40} +5400.95 q^{41} +19686.6 q^{43} +(-10895.9 + 18872.3i) q^{44} +(893.900 + 1548.28i) q^{45} +(-4385.88 - 7596.57i) q^{46} +(1028.28 - 1781.04i) q^{47} -335.921 q^{48} +24218.7 q^{50} +(6189.98 - 10721.4i) q^{51} +(20863.5 + 36136.7i) q^{52} +(-9011.37 - 15608.2i) q^{53} +(-3346.56 + 5796.41i) q^{54} -9197.45 q^{55} +20817.2 q^{57} +(-32296.3 + 55938.8i) q^{58} +(3717.84 + 6439.49i) q^{59} +(-5194.05 - 8996.36i) q^{60} +(1747.69 - 3027.09i) q^{61} +11579.3 q^{62} -52792.5 q^{64} +(-8805.67 + 15251.9i) q^{65} +(-17216.6 - 29820.0i) q^{66} +(-7928.21 - 13732.1i) q^{67} +(-35967.2 + 62297.0i) q^{68} +8598.62 q^{69} +58133.5 q^{71} +(7546.48 - 13070.9i) q^{72} +(19555.3 + 33870.8i) q^{73} +(44879.9 + 77734.2i) q^{74} +(-11870.3 + 20560.0i) q^{75} -120960. q^{76} -65932.8 q^{78} +(-4880.35 + 8453.01i) q^{79} +(411.906 + 713.442i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(24793.7 - 42943.9i) q^{82} +70395.7 q^{83} -30360.6 q^{85} +(90373.4 - 156531. i) q^{86} +(-31658.8 - 54834.7i) q^{87} +(38823.3 + 67243.9i) q^{88} +(72153.1 - 124973. i) q^{89} +16414.2 q^{90} -49962.7 q^{92} +(-5675.36 + 9830.01i) q^{93} +(-9440.90 - 16352.1i) q^{94} +(-25526.1 - 44212.5i) q^{95} +(25289.8 - 43803.3i) q^{96} +79328.7 q^{97} +33753.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9 + 283 * q^10 - 402 * q^11 + 621 * q^12 - 924 * q^13 - 3273 * q^16 + 276 * q^17 - 243 * q^18 + 510 * q^19 - 9438 * q^20 + 2750 * q^22 - 6900 * q^23 + 1107 * q^24 - 2814 * q^25 - 15138 * q^26 - 5832 * q^27 + 1080 * q^29 - 2547 * q^30 - 6410 * q^31 - 15519 * q^32 + 3618 * q^33 - 42288 * q^34 + 11178 * q^36 - 15250 * q^37 - 41250 * q^38 - 4158 * q^39 - 8547 * q^40 - 8616 * q^41 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 58914 * q^48 - 14604 * q^50 - 2484 * q^51 - 47476 * q^52 - 13692 * q^53 + 2187 * q^54 - 146248 * q^55 + 9180 * q^57 - 52309 * q^58 + 34830 * q^59 - 42471 * q^60 - 5364 * q^61 - 32058 * q^62 - 146974 * q^64 - 66864 * q^65 + 12375 * q^66 + 5994 * q^67 - 58272 * q^68 - 124200 * q^69 + 178536 * q^71 - 9963 * q^72 + 59638 * q^73 + 185442 * q^74 + 25326 * q^75 - 42616 * q^76 - 272484 * q^78 + 44062 * q^79 - 33381 * q^80 - 26244 * q^81 + 57596 * q^82 + 416892 * q^83 + 72648 * q^85 + 136968 * q^86 + 4860 * q^87 - 87597 * q^88 - 77520 * q^89 - 45846 * q^90 + 316512 * q^92 + 57690 * q^93 - 73722 * q^94 + 221376 * q^95 + 139671 * q^96 + 377260 * q^97 + 65124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.59061	−	7.95118i	0.811514	−	1.40558i	−0.100291	−	0.994958i	$-0.531977\pi$
$2$	4.59061	−	7.95118i	0.811514	−	1.40558i	0.911804	−	0.410625i	$-0.134689\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−26.1475	−	45.2888i	−0.817109	−	1.41527i
$5$	11.0358	−	19.1146i	0.197414	−	0.341932i	−0.750275	−	0.661126i	$-0.770079\pi$
$5$	11.0358	−	19.1146i	0.197414	−	0.341932i	0.947689	+	0.319194i	$0.103412\pi$
$6$	82.6311			0.937055
$7$		0			0
$7$		0			0
$8$	−186.333			−1.02935
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−101.322	−	175.495i	−0.320409	−	0.554965i
$11$	−208.355	−	360.881i	−0.519184	−	0.899254i	−0.999751	−	0.0222959i	$-0.992902\pi$
$11$	−208.355	−	360.881i	−0.519184	−	0.899254i	0.480567	−	0.876958i	$-0.340431\pi$
$12$	235.327	−	407.599i	0.471758	−	0.817109i
$13$	−797.918			−1.30948			−0.654742	−	0.755853i	$-0.727223\pi$
$13$	−797.918			−1.30948			−0.654742	+	0.755853i	$0.727223\pi$
$14$		0			0
$15$	198.644			0.227955
$16$	−18.6623	+	32.3240i	−0.0182249	+	0.0315664i
$17$	−687.775	−	1191.26i	−0.577197	−	0.999735i	−0.995799	−	0.0915652i	$-0.970813\pi$
$17$	−687.775	−	1191.26i	−0.577197	−	0.999735i	0.418602	−	0.908170i	$-0.362520\pi$
$18$	371.840	+	644.045i	0.270505	+	0.468528i
$19$	1156.51	−	2003.14i	0.734965	−	1.27300i	−0.219774	−	0.975551i	$-0.570532\pi$
$19$	1156.51	−	2003.14i	0.734965	−	1.27300i	0.954739	−	0.297446i	$-0.0961347\pi$
$20$	−1154.23			−0.645236
$21$		0			0
$22$	−3825.91			−1.68530
$23$	477.701	−	827.402i	0.188294	−	0.326135i	−0.756388	−	0.654124i	$-0.773038\pi$
$23$	477.701	−	827.402i	0.188294	−	0.326135i	0.944682	+	0.327989i	$0.106371\pi$
$24$	−838.497	−	1452.32i	−0.297149	−	0.514676i
$25$	1318.92	+	2284.44i	0.422055	+	0.731021i
$26$	−3662.93	+	6344.39i	−1.06266	+	1.84059i
$27$	−729.000			−0.192450
$28$		0			0
$29$	−7035.29			−1.55341			−0.776707	−	0.629862i	$-0.783111\pi$
$29$	−7035.29			−1.55341			−0.776707	+	0.629862i	$0.783111\pi$
$30$	911.900	−	1579.46i	0.184988	−	0.320409i
$31$	630.596	+	1092.22i	0.117855	+	0.204130i	0.918917	−	0.394450i	$-0.129065\pi$
$31$	630.596	+	1092.22i	0.117855	+	0.204130i	−0.801063	+	0.598581i	$0.795732\pi$
$32$	−2809.98	−	4867.03i	−0.485097	−	0.840212i
$33$	1875.19	−	3247.93i	0.299751	−	0.519184i
$34$	−12629.2			−1.87361
$35$		0			0
$36$	4235.89			0.544739
$37$	−4888.22	+	8466.65i	−0.587012	+	1.01673i	0.407610	+	0.913156i	$0.366362\pi$
$37$	−4888.22	+	8466.65i	−0.587012	+	1.01673i	−0.994621	+	0.103578i	$0.966971\pi$
$38$	−10618.2	−	18391.3i	−1.19287	−	2.06611i
$39$	−3590.63	−	6219.16i	−0.378015	−	0.654742i
$40$	−2056.33	+	3561.67i	−0.203209	+	0.351968i
$41$	5400.95			0.501777			0.250888	−	0.968016i	$-0.419277\pi$
$41$	5400.95			0.501777			0.250888	+	0.968016i	$0.419277\pi$
$42$		0			0
$43$	19686.6			1.62367			0.811837	−	0.583885i	$-0.198468\pi$
$43$	19686.6			1.62367			0.811837	+	0.583885i	$0.198468\pi$
$44$	−10895.9	+	18872.3i	−0.848460	+	1.46958i
$45$	893.900	+	1548.28i	0.0658048	+	0.113977i
$46$	−4385.88	−	7596.57i	−0.305606	−	0.529326i
$47$	1028.28	−	1781.04i	0.0678997	−	0.117606i	−0.830077	−	0.557649i	$-0.811704\pi$
$47$	1028.28	−	1781.04i	0.0678997	−	0.117606i	0.897977	+	0.440043i	$0.145037\pi$
$48$	−335.921			−0.0210443
$49$		0			0
$50$	24218.7			1.37001
$51$	6189.98	−	10721.4i	0.333245	−	0.577197i
$52$	20863.5	+	36136.7i	1.06999	+	1.85328i
$53$	−9011.37	−	15608.2i	−0.440658	−	0.763241i	0.557081	−	0.830458i	$-0.311921\pi$
$53$	−9011.37	−	15608.2i	−0.440658	−	0.763241i	−0.997738	+	0.0672170i	$0.978588\pi$
$54$	−3346.56	+	5796.41i	−0.156176	+	0.270505i
$55$	−9197.45			−0.409978
$56$		0			0
$57$	20817.2			0.848664
$58$	−32296.3	+	55938.8i	−1.26062	+	2.18345i
$59$	3717.84	+	6439.49i	0.139047	+	0.240836i	0.927136	−	0.374725i	$-0.122263\pi$
$59$	3717.84	+	6439.49i	0.139047	+	0.240836i	−0.788089	+	0.615561i	$0.788930\pi$
$60$	−5194.05	−	8996.36i	−0.186264	−	0.322618i
$61$	1747.69	−	3027.09i	0.0601368	−	0.104160i	−0.834390	−	0.551175i	$-0.814180\pi$
$61$	1747.69	−	3027.09i	0.0601368	−	0.104160i	0.894526	+	0.447015i	$0.147513\pi$
$62$	11579.3			0.382563
$63$		0			0
$64$	−52792.5			−1.61110
$65$	−8805.67	+	15251.9i	−0.258511	+	0.447754i
$66$	−17216.6	−	29820.0i	−0.486505	−	0.842651i
$67$	−7928.21	−	13732.1i	−0.215769	−	0.373722i	0.737741	−	0.675083i	$-0.235892\pi$
$67$	−7928.21	−	13732.1i	−0.215769	−	0.373722i	−0.953510	+	0.301361i	$0.902559\pi$
$68$	−35967.2	+	62297.0i	−0.943266	+	1.63378i
$69$	8598.62			0.217423
$70$		0			0
$71$	58133.5			1.36861			0.684306	−	0.729195i	$-0.260105\pi$
$71$	58133.5			1.36861			0.684306	+	0.729195i	$0.260105\pi$
$72$	7546.48	−	13070.9i	0.171559	−	0.297149i
$73$	19555.3	+	33870.8i	0.429495	+	0.743907i	0.996828	−	0.0795812i	$-0.0253583\pi$
$73$	19555.3	+	33870.8i	0.429495	+	0.743907i	−0.567334	+	0.823488i	$0.692025\pi$
$74$	44879.9	+	77734.2i	0.952736	+	1.65019i
$75$	−11870.3	+	20560.0i	−0.243674	+	0.422055i
$76$	−120960.			−2.40218
$77$		0			0
$78$	−65932.8			−1.22706
$79$	−4880.35	+	8453.01i	−0.0879798	+	0.152385i	−0.906657	−	0.421868i	$-0.861374\pi$
$79$	−4880.35	+	8453.01i	−0.0879798	+	0.152385i	0.818677	+	0.574254i	$0.194708\pi$
$80$	411.906	+	713.442i	0.00719570	+	0.0124633i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	24793.7	−	42943.9i	0.407199	−	0.705289i
$83$	70395.7			1.12163			0.560816	−	0.827940i	$-0.310487\pi$
$83$	70395.7			1.12163			0.560816	+	0.827940i	$0.310487\pi$
$84$		0			0
$85$	−30360.6			−0.455788
$86$	90373.4	−	156531.i	1.31763	−	2.28221i
$87$	−31658.8	−	54834.7i	−0.448432	−	0.776707i
$88$	38823.3	+	67243.9i	0.534424	+	0.925649i
$89$	72153.1	−	124973.i	0.965562	−	1.67240i	0.257464	−	0.966288i	$-0.417113\pi$
$89$	72153.1	−	124973.i	0.965562	−	1.67240i	0.708098	−	0.706115i	$-0.249554\pi$
$90$	16414.2			0.213606
$91$		0			0
$92$	−49962.7			−0.615427
$93$	−5675.36	+	9830.01i	−0.0680434	+	0.117855i
$94$	−9440.90	−	16352.1i	−0.110203	−	0.190877i
$95$	−25526.1	−	44212.5i	−0.290185	−	0.502616i
$96$	25289.8	−	43803.3i	0.280071	−	0.485097i
$97$	79328.7			0.856053			0.428027	−	0.903766i	$-0.359209\pi$
$97$	79328.7			0.856053			0.428027	+	0.903766i	$0.359209\pi$
$98$		0			0
$99$	33753.5			0.346123
$100$	68973.0	−	119465.i	0.689730	−	1.19465i
$101$	−42416.9	−	73468.2i	−0.413747	−	0.716631i	0.581549	−	0.813512i	$-0.302447\pi$
$101$	−42416.9	−	73468.2i	−0.413747	−	0.716631i	−0.995296	+	0.0968802i	$0.969114\pi$
$102$	−56831.6	−	98435.2i	−0.540866	−	0.936807i
$103$	10166.1	−	17608.3i	0.0944197	−	0.163540i	−0.814947	−	0.579536i	$-0.803234\pi$
$103$	10166.1	−	17608.3i	0.0944197	−	0.163540i	0.909366	+	0.415996i	$0.136567\pi$
$104$	148678.			1.34792
$105$		0			0
$106$	−165471.			−1.43040
$107$	−3481.09	+	6029.43i	−0.0293938	+	0.0509116i	−0.880348	−	0.474328i	$-0.842691\pi$
$107$	−3481.09	+	6029.43i	−0.0293938	+	0.0509116i	0.850954	+	0.525240i	$0.176024\pi$
$108$	19061.5	+	33015.5i	0.157253	+	0.272370i
$109$	−56325.7	−	97559.0i	−0.454088	−	0.786504i	0.544547	−	0.838730i	$-0.316702\pi$
$109$	−56325.7	−	97559.0i	−0.454088	−	0.786504i	−0.998635	+	0.0522262i	$0.983368\pi$
$110$	−42221.9	+	73130.5i	−0.332703	+	0.576258i
$111$	−87988.0			−0.677823
$112$		0			0
$113$	112005.			0.825167			0.412583	−	0.910920i	$-0.364627\pi$
$113$	112005.			0.825167			0.412583	+	0.910920i	$0.364627\pi$
$114$	95563.9	−	165522.i	0.688703	−	1.19287i
$115$	−10543.6	−	18262.1i	−0.0743439	−	0.128767i
$116$	183955.	+	318620.i	1.26931	+	2.19851i
$117$	32315.7	−	55972.4i	0.218247	−	0.378015i
$118$	68268.7			0.451353
$119$		0			0
$120$	−37014.0			−0.234646
$121$	−6297.91	+	10908.3i	−0.0391051	+	0.0677320i
$122$	−16046.0	−	27792.4i	−0.0976037	−	0.169055i
$123$	24304.3	+	42096.2i	0.144850	+	0.250888i
$124$	32977.0	−	57117.8i	0.192600	−	0.333593i
$125$	127195.			0.728108
$126$		0			0
$127$	82224.5			0.452368			0.226184	−	0.974085i	$-0.427375\pi$
$127$	82224.5			0.452368			0.226184	+	0.974085i	$0.427375\pi$
$128$	−152431.	+	264018.i	−0.822333	+	1.42432i
$129$	88589.5	+	153442.i	0.468714	+	0.811837i
$130$	80846.8	+	140031.i	0.419570	+	0.726717i
$131$	−87905.9	+	152258.i	−0.447548	+	0.775176i	−0.998226	−	0.0595417i	$-0.981036\pi$
$131$	−87905.9	+	152258.i	−0.447548	+	0.775176i	0.550677	+	0.834718i	$0.314369\pi$
$132$	−196126.			−0.979718
$133$		0			0
$134$	−145581.			−0.700397
$135$	−8045.10	+	13934.5i	−0.0379924	+	0.0658048i
$136$	128155.	+	221971.i	0.594140	+	1.02908i
$137$	−15665.2	−	27132.9i	−0.0713072	−	0.123508i	0.828167	−	0.560481i	$-0.189384\pi$
$137$	−15665.2	−	27132.9i	−0.0713072	−	0.123508i	−0.899474	+	0.436973i	$0.856050\pi$
$138$	39472.9	−	68369.1i	0.176442	−	0.305606i
$139$	−152234.			−0.668305			−0.334152	−	0.942519i	$-0.608450\pi$
$139$	−152234.			−0.668305			−0.334152	+	0.942519i	$0.608450\pi$
$140$		0			0
$141$	18509.1			0.0784038
$142$	266868.	−	462229.i	1.11065	−	1.92370i
$143$	166250.	+	287953.i	0.679863	+	1.17756i
$144$	−1511.64	−	2618.24i	−0.00607495	−	0.0105221i
$145$	−77640.1	+	134477.i	−0.306666	+	0.531162i
$146$	359084.			1.39416
$147$		0			0
$148$	511259.			1.91861
$149$	−181430.	+	314246.i	−0.669489	+	1.15959i	0.308558	+	0.951206i	$0.400154\pi$
$149$	−181430.	+	314246.i	−0.669489	+	1.15959i	−0.978047	+	0.208384i	$0.933180\pi$
$150$	108984.	+	188766.i	0.395489	+	0.685007i
$151$	−102563.	−	177644.i	−0.366056	−	0.634027i	0.622889	−	0.782310i	$-0.285959\pi$
$151$	−102563.	−	177644.i	−0.366056	−	0.634027i	−0.988945	+	0.148283i	$0.952625\pi$
$152$	−215496.	+	373250.i	−0.756538	+	1.31036i
$153$	111420.			0.384798
$154$		0			0
$155$	27836.5			0.0930648
$156$	−187772.	+	325231.i	−0.617759	+	1.06999i
$157$	−38636.0	−	66919.5i	−0.125096	−	0.216672i	0.796675	−	0.604409i	$-0.206591\pi$
$157$	−38636.0	−	66919.5i	−0.125096	−	0.216672i	−0.921770	+	0.387736i	$0.873257\pi$
$158$	44807.6	+	77609.0i	0.142794	+	0.247326i
$159$	81102.3	−	140473.i	0.254414	−	0.440658i
$160$	−124042.			−0.383060
$161$		0			0
$162$	−60238.0			−0.180336
$163$	−92465.7	+	160155.i	−0.272591	+	0.472141i	−0.969525	−	0.244994i	$-0.921214\pi$
$163$	−92465.7	+	160155.i	−0.272591	+	0.472141i	0.696934	+	0.717136i	$0.254547\pi$
$164$	−141221.	−	244602.i	−0.410006	−	0.710152i
$165$	−41388.5	−	71687.0i	−0.118350	−	0.204989i
$166$	323159.	−	559728.i	0.910220	−	1.57655i
$167$	−129262.			−0.358657			−0.179329	−	0.983789i	$-0.557393\pi$
$167$	−129262.			−0.358657			−0.179329	+	0.983789i	$0.557393\pi$
$168$		0			0
$169$	265380.			0.714746
$170$	−139374.	+	241403.i	−0.369878	+	0.640648i
$171$	93677.6	+	162254.i	0.244988	+	0.424332i
$172$	−514754.	−	891580.i	−1.32672	−	2.29794i
$173$	−253934.	+	439826.i	−0.645067	+	1.11729i	0.339219	+	0.940707i	$0.389837\pi$
$173$	−253934.	+	439826.i	−0.645067	+	1.11729i	−0.984286	+	0.176582i	$0.943496\pi$
$174$	−581334.			−1.45563
$175$		0			0
$176$	15553.5			0.0378483
$177$	−33460.6	+	57955.4i	−0.0802786	+	0.139047i
$178$	−662454.	−	1.14740e6i	−1.56713	−	2.71435i
$179$	66294.5	+	114825.i	0.154648	+	0.267859i	0.932931	−	0.360056i	$-0.117242\pi$
$179$	66294.5	+	114825.i	0.154648	+	0.267859i	−0.778283	+	0.627914i	$0.783909\pi$
$180$	46746.5	−	80967.3i	0.107539	−	0.186264i
$181$	740060.			1.67908			0.839538	−	0.543301i	$-0.182826\pi$
$181$	740060.			1.67908			0.839538	+	0.543301i	$0.182826\pi$
$182$		0			0
$183$	31458.5			0.0694400
$184$	−89011.3	+	154172.i	−0.193821	+	0.335708i
$185$	107891.	+	186873.i	0.231769	+	0.401436i
$186$	52106.8	+	90251.6i	0.110436	+	0.191281i
$187$	−286603.	+	496410.i	−0.599344	+	1.03809i
$188$	−107548.			−0.221926
$189$		0			0
$190$	−468722.			−0.941957
$191$	291366.	−	504661.i	0.577904	−	1.00096i	−0.417815	−	0.908532i	$-0.637204\pi$
$191$	291366.	−	504661.i	0.577904	−	1.00096i	0.995719	−	0.0924273i	$-0.0294626\pi$
$192$	−237566.	−	411477.i	−0.465085	−	0.805550i
$193$	200452.	+	347193.i	0.387362	+	0.670931i	0.992094	−	0.125498i	$-0.0400529\pi$
$193$	200452.	+	347193.i	0.387362	+	0.670931i	−0.604731	+	0.796429i	$0.706720\pi$
$194$	364167.	−	630756.i	0.694699	−	1.20325i
$195$	−158502.			−0.298503
$196$		0			0
$197$	671589.			1.23293			0.616464	−	0.787383i	$-0.288564\pi$
$197$	671589.			1.23293			0.616464	+	0.787383i	$0.288564\pi$
$198$	154949.	−	268380.i	0.280884	−	0.486505i
$199$	−227511.	−	394060.i	−0.407258	−	0.705391i	0.587324	−	0.809352i	$-0.300182\pi$
$199$	−227511.	−	394060.i	−0.407258	−	0.705391i	−0.994581	+	0.103961i	$0.966848\pi$
$200$	−245758.	−	425666.i	−0.434443	−	0.752478i
$201$	71353.9	−	123589.i	0.124574	−	0.215769i
$202$	−778878.			−1.34305
$203$		0			0
$204$	−647409.			−1.08919
$205$	59603.8	−	103237.i	0.0990580	−	0.171573i
$206$	−93337.6	−	161665.i	−0.153246	−	0.265430i
$207$	38693.8	+	67019.6i	0.0627647	+	0.108712i
$208$	14891.0	−	25791.9i	0.0238652	−	0.0413357i
$209$	−963860.			−1.52633
$210$		0			0
$211$	−1.19545e6			−1.84852			−0.924260	−	0.381764i	$-0.875317\pi$
$211$	−1.19545e6			−1.84852			−0.924260	+	0.381764i	$0.875317\pi$
$212$	−471249.	+	816228.i	−0.720130	+	1.24730i
$213$	261601.	+	453105.i	0.395084	+	0.684306i
$214$	31960.7	+	55357.6i	0.0477070	+	0.0826310i
$215$	217257.	−	376300.i	0.320537	−	0.555186i
$216$	135837.			0.198099
$217$		0			0
$218$	−1.03428e6			−1.47400
$219$	−175998.	+	304837.i	−0.247969	+	0.429495i
$220$	240490.	+	416541.i	0.334997	+	0.580231i
$221$	548788.	+	950529.i	0.755830	+	1.30914i
$222$	−403919.	+	699608.i	−0.550062	+	0.952736i
$223$	−296529.			−0.399305			−0.199653	−	0.979867i	$-0.563981\pi$
$223$	−296529.			−0.399305			−0.199653	+	0.979867i	$0.563981\pi$
$224$		0			0
$225$	−213665.			−0.281370
$226$	514172.	−	890573.i	0.669634	−	1.15984i
$227$	109073.	+	188920.i	0.140492	+	0.243340i	0.927682	−	0.373371i	$-0.121798\pi$
$227$	109073.	+	188920.i	0.140492	+	0.243340i	−0.787190	+	0.616711i	$0.788465\pi$
$228$	−544318.	−	942787.i	−0.693451	−	1.20109i
$229$	−614602.	+	1.06452e6i	−0.774471	+	1.34142i	0.160620	+	0.987016i	$0.448651\pi$
$229$	−614602.	+	1.06452e6i	−0.774471	+	1.34142i	−0.935091	+	0.354407i	$0.884683\pi$
$230$	−193607.			−0.241324
$231$		0			0
$232$	1.31090e6			1.59901
$233$	31472.1	−	54511.3i	0.0379784	−	0.0657805i	−0.846411	−	0.532530i	$-0.821242\pi$
$233$	31472.1	−	54511.3i	0.0379784	−	0.0657805i	0.884390	+	0.466749i	$0.154575\pi$
$234$	−296698.	−	513895.i	−0.354221	−	0.613529i
$235$	−22695.8	−	39310.4i	−0.0268088	−	0.0464341i
$236$	194424.	−	336753.i	0.227233	−	0.393578i
$237$	−87846.2			−0.101590
$238$		0			0
$239$	219330.			0.248372			0.124186	−	0.992259i	$-0.460368\pi$
$239$	219330.			0.248372			0.124186	+	0.992259i	$0.460368\pi$
$240$	−3707.15	+	6420.98i	−0.00415444	+	0.00719570i
$241$	216932.	+	375737.i	0.240592	+	0.416717i	0.960883	−	0.276955i	$-0.0893252\pi$
$241$	216932.	+	375737.i	0.240592	+	0.416717i	−0.720291	+	0.693672i	$0.755992\pi$
$242$	57822.6	+	100152.i	0.0634686	+	0.109931i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	−182791.			−0.196553
$245$		0			0
$246$	446286.			0.470193
$247$	−922803.	+	1.59834e6i	−0.962424	+	1.66697i
$248$	−117501.	−	203517.i	−0.121314	−	0.210122i
$249$	316780.	+	548680.i	0.323787	+	0.560816i
$250$	583904.	−	1.01135e6i	0.590870	−	1.02342i
$251$	1.71109e6			1.71431			0.857155	−	0.515059i	$-0.172230\pi$
$251$	1.71109e6			1.71431			0.857155	+	0.515059i	$0.172230\pi$
$252$		0			0
$253$	−398125.			−0.391037
$254$	377461.	−	653782.i	0.367103	−	0.635841i
$255$	−136623.	−	236638.i	−0.131575	−	0.227894i
$256$	554822.	+	960979.i	0.529119	+	0.916461i
$257$	492029.	−	852219.i	0.464684	−	0.804856i	−0.534503	−	0.845166i	$-0.679501\pi$
$257$	492029.	−	852219.i	0.464684	−	0.804856i	0.999187	+	0.0403103i	$0.0128346\pi$
$258$	1.62672e6			1.52147
$259$		0			0
$260$	920984.			0.844926
$261$	284929.	−	493512.i	0.258902	−	0.448432i
$262$	807084.	+	1.39791e6i	0.726383	+	1.25813i
$263$	−273548.	−	473799.i	−0.243862	−	0.422381i	0.717949	−	0.696096i	$-0.245081\pi$
$263$	−273548.	−	473799.i	−0.243862	−	0.422381i	−0.961811	+	0.273714i	$0.911748\pi$
$264$	−349410.	+	605196.i	−0.308550	+	0.534424i
$265$	−397791.			−0.347969
$266$		0			0
$267$	1.29876e6			1.11493
$268$	−414605.	+	718118.i	−0.352613	+	0.610743i
$269$	−320556.	−	555219.i	−0.270099	−	0.467825i	0.698788	−	0.715329i	$-0.253723\pi$
$269$	−320556.	−	555219.i	−0.270099	−	0.467825i	−0.968887	+	0.247504i	$0.920390\pi$
$270$	73863.9	+	127936.i	0.0616627	+	0.106803i
$271$	−274006.	+	474593.i	−0.226640	+	0.392552i	−0.956810	−	0.290713i	$-0.906107\pi$
$271$	−274006.	+	474593.i	−0.226640	+	0.392552i	0.730170	+	0.683265i	$0.239441\pi$
$272$	51341.8			0.0420774
$273$		0			0
$274$	−287651.			−0.231467
$275$	549607.	−	951948.i	0.438249	−	0.759069i
$276$	−224832.	−	389421.i	−0.177658	−	0.307713i
$277$	−837070.	−	1.44985e6i	−0.655485	−	1.13533i	−0.981772	−	0.190062i	$-0.939131\pi$
$277$	−837070.	−	1.44985e6i	−0.655485	−	1.13533i	0.326287	−	0.945271i	$-0.394202\pi$
$278$	−698847.	+	1.21044e6i	−0.542338	+	0.939358i
$279$	−102157.			−0.0785698
$280$		0			0
$281$	1.81078e6			1.36804			0.684021	−	0.729462i	$-0.260230\pi$
$281$	1.81078e6			1.36804			0.684021	+	0.729462i	$0.260230\pi$
$282$	84968.1	−	147169.i	0.0636258	−	0.110203i
$283$	1.25657e6	+	2.17645e6i	0.932657	+	1.61541i	0.778759	+	0.627323i	$0.215849\pi$
$283$	1.25657e6	+	2.17645e6i	0.932657	+	1.61541i	0.153898	+	0.988087i	$0.450817\pi$
$284$	−1.52004e6	−	2.63279e6i	−1.11830	−	1.93696i
$285$	229735.	−	397913.i	0.167539	−	0.290185i
$286$	3.05276e6			2.20687
$287$		0			0
$288$	455217.			0.323398
$289$	−236142.	+	409009.i	−0.166314	+	0.288064i
$290$	712831.	+	1.23466e6i	0.497728	+	0.862090i
$291$	356979.	+	618306.i	0.247121	+	0.428027i
$292$	1.02265e6	−	1.77127e6i	0.701888	−	1.21571i
$293$	−107228.			−0.0729691			−0.0364845	−	0.999334i	$-0.511616\pi$
$293$	−107228.			−0.0729691			−0.0364845	+	0.999334i	$0.511616\pi$
$294$		0			0
$295$	164117.			0.109799
$296$	910836.	−	1.57761e6i	0.604242	−	1.04658i
$297$	151891.	+	263082.i	0.0999171	+	0.173061i
$298$	1.66575e6	+	2.88517e6i	1.08660	+	1.88205i
$299$	−381166.	+	660199.i	−0.246568	+	0.427068i
$300$	1.24151e6			0.796431
$301$		0			0
$302$	−1.88330e6			−1.18824
$303$	381752.	−	661214.i	0.238877	−	0.413747i
$304$	43166.3	+	74766.2i	0.0267893	+	0.0464004i
$305$	−38574.4	−	66812.8i	−0.0237437	−	0.0411254i
$306$	511485.	−	885917.i	0.312269	−	0.540866i
$307$	−1.49622e6			−0.906042			−0.453021	−	0.891500i	$-0.649654\pi$
$307$	−1.49622e6			−0.906042			−0.453021	+	0.891500i	$0.649654\pi$
$308$		0			0
$309$	182990.			0.109027
$310$	127787.	−	221333.i	0.0755234	−	0.130810i
$311$	430601.	+	745823.i	0.252449	+	0.437255i	0.964200	−	0.265178i	$-0.0854306\pi$
$311$	430601.	+	745823.i	0.252449	+	0.437255i	−0.711750	+	0.702433i	$0.752097\pi$
$312$	669052.	+	1.15883e6i	0.389111	+	0.673960i
$313$	−251969.	+	436422.i	−0.145374	+	0.251794i	−0.929512	−	0.368791i	$-0.879772\pi$
$313$	−251969.	+	436422.i	−0.145374	+	0.251794i	0.784139	+	0.620586i	$0.213105\pi$
$314$	−709452.			−0.406068
$315$		0			0
$316$	510435.			0.287556
$317$	240004.	−	415700.i	0.134144	−	0.232344i	−0.791126	−	0.611653i	$-0.790505\pi$
$317$	240004.	−	415700.i	0.134144	−	0.232344i	0.925270	+	0.379309i	$0.123838\pi$
$318$	−744619.	−	1.28972e6i	−0.412921	−	0.715199i
$319$	1.46584e6	+	2.53890e6i	0.806508	+	1.39691i
$320$	−582608.	+	1.00911e6i	−0.318055	+	0.550887i
$321$	−62659.7			−0.0339411
$322$		0			0
$323$	−3.18168e6			−1.69688
$324$	−171554.	+	297140.i	−0.0907899	+	0.157253i
$325$	−1.05239e6	−	1.82280e6i	−0.552674	−	0.957259i
$326$	848948.	+	1.47042e6i	0.442423	+	0.766298i
$327$	506931.	−	878031.i	0.262168	−	0.454088i
$328$	−1.00637e6			−0.516505
$329$		0			0
$330$	−759995.			−0.384172
$331$	1.09961e6	−	1.90458e6i	0.551656	−	0.955497i	−0.446499	−	0.894784i	$-0.647329\pi$
$331$	1.09961e6	−	1.90458e6i	0.551656	−	0.955497i	0.998155	−	0.0607125i	$-0.0193373\pi$
$332$	−1.84067e6	−	3.18813e6i	−0.916496	−	1.58742i
$333$	−395946.	−	685799.i	−0.195671	−	0.338911i
$334$	−593392.	+	1.02778e6i	−0.291055	+	0.504122i
$335$	−349977.			−0.170383
$336$		0			0
$337$	−1.35725e6			−0.651008			−0.325504	−	0.945541i	$-0.605534\pi$
$337$	−1.35725e6			−0.651008			−0.325504	+	0.945541i	$0.605534\pi$
$338$	1.21826e6	−	2.11008e6i	0.580026	−	1.00463i
$339$	504023.	+	872993.i	0.238205	+	0.412583i
$340$	793854.	+	1.37499e6i	0.372429	+	0.645065i
$341$	262775.	−	455140.i	0.122377	−	0.211963i
$342$	1.72015e6			0.795245
$343$		0			0
$344$	−3.66825e6			−1.67133
$345$	94892.6	−	164359.i	0.0429225	−	0.0743439i
$346$	2.33142e6	+	4.03814e6i	1.04696	+	1.81339i
$347$	−1.89970e6	−	3.29038e6i	−0.846959	−	1.46698i	−0.883909	−	0.467658i	$-0.845098\pi$
$347$	−1.89970e6	−	3.29038e6i	−0.846959	−	1.46698i	0.0369507	−	0.999317i	$-0.488236\pi$
$348$	−1.65560e6	+	2.86758e6i	−0.732835	+	1.26931i
$349$	1.31753e6			0.579024			0.289512	−	0.957174i	$-0.406507\pi$
$349$	1.31753e6			0.579024			0.289512	+	0.957174i	$0.406507\pi$
$350$		0			0
$351$	581682.			0.252010
$352$	−1.17095e6	+	2.02814e6i	−0.503710	+	0.872451i
$353$	−1.71253e6	−	2.96618e6i	−0.731477	−	1.26695i	−0.956252	−	0.292544i	$-0.905498\pi$
$353$	−1.71253e6	−	2.96618e6i	−0.731477	−	1.26695i	0.224775	−	0.974411i	$-0.427835\pi$
$354$	307209.	+	532102.i	0.130294	+	0.225677i
$355$	641549.	−	1.11120e6i	0.270184	−	0.467972i
$356$	−7.54649e6			−3.15588
$357$		0			0
$358$	1.21733e6			0.501997
$359$	−735419.	+	1.27378e6i	−0.301161	+	0.521626i	−0.976399	−	0.215974i	$-0.930707\pi$
$359$	−735419.	+	1.27378e6i	−0.301161	+	0.521626i	0.675238	+	0.737600i	$0.264041\pi$
$360$	−166563.	−	288495.i	−0.0677364	−	0.117323i
$361$	−1.43700e6	−	2.48895e6i	−0.580347	−	1.00519i
$362$	3.39733e6	−	5.88435e6i	1.36259	−	2.36008i
$363$	−113362.			−0.0451547
$364$		0			0
$365$	863235.			0.339154
$366$	144414.	−	250132.i	0.0563515	−	0.0976037i
$367$	−2.49039e6	−	4.31349e6i	−0.965168	−	1.67172i	−0.709163	−	0.705045i	$-0.750927\pi$
$367$	−2.49039e6	−	4.31349e6i	−0.965168	−	1.67172i	−0.256006	−	0.966675i	$-0.582407\pi$
$368$	17830.0	+	30882.4i	0.00686326	+	0.0118875i
$369$	−218738.	+	378866.i	−0.0836295	+	0.144850i
$370$	1.98114e6			0.752335
$371$		0			0
$372$	593586.			0.222396
$373$	−1.98024e6	+	3.42987e6i	−0.736962	+	1.27646i	0.216895	+	0.976195i	$0.430407\pi$
$373$	−1.98024e6	+	3.42987e6i	−0.736962	+	1.27646i	−0.953857	+	0.300261i	$0.902926\pi$
$374$	2.63136e6	+	4.55766e6i	0.972751	+	1.68485i
$375$	572379.	+	991389.i	0.210187	+	0.364054i
$376$	−191603.	+	331866.i	−0.0698927	+	0.121058i
$377$	5.61359e6			2.03417
$378$		0			0
$379$	−1.75155e6			−0.626359			−0.313179	−	0.949694i	$-0.601394\pi$
$379$	−1.75155e6			−0.626359			−0.313179	+	0.949694i	$0.601394\pi$
$380$	−1.33489e6	+	2.31209e6i	−0.474226	+	0.821384i
$381$	370010.	+	640876.i	0.130587	+	0.226184i
$382$	−2.67510e6	−	4.63341e6i	−0.937954	−	1.62458i
$383$	1.56917e6	−	2.71788e6i	0.546604	−	0.946745i	−0.451900	−	0.892068i	$-0.649254\pi$
$383$	1.56917e6	−	2.71788e6i	0.546604	−	0.946745i	0.998504	−	0.0546771i	$-0.0174129\pi$
$384$	−2.74375e6			−0.949549
$385$		0			0
$386$	3.68079e6			1.25740
$387$	−797306.	+	1.38097e6i	−0.270612	+	0.468714i
$388$	−2.07425e6	−	3.59270e6i	−0.699489	−	1.21155i
$389$	526262.	+	911512.i	0.176331	+	0.305414i	0.940621	−	0.339459i	$-0.110244\pi$
$389$	526262.	+	911512.i	0.176331	+	0.305414i	−0.764290	+	0.644872i	$0.776911\pi$
$390$	−727622.	+	1.26028e6i	−0.242239	+	0.419570i
$391$	−1.31420e6			−0.434731
$392$		0			0
$393$	−1.58231e6			−0.516784
$394$	3.08301e6	−	5.33992e6i	1.00054	−	1.73298i
$395$	107717.	+	186571.i	0.0347370	+	0.0601662i
$396$	−882568.	−	1.52865e6i	−0.282820	−	0.489859i
$397$	227362.	−	393803.i	0.0724005	−	0.125401i	−0.827552	−	0.561389i	$-0.810267\pi$
$397$	227362.	−	393803.i	0.0724005	−	0.125401i	0.899953	+	0.435987i	$0.143601\pi$
$398$	−4.17766e6			−1.32198
$399$		0			0
$400$	−98456.3			−0.0307676
$401$	1.44216e6	−	2.49789e6i	0.447870	−	0.775733i	−0.550378	−	0.834916i	$-0.685516\pi$
$401$	1.44216e6	−	2.49789e6i	0.447870	−	0.775733i	0.998247	+	0.0591831i	$0.0188496\pi$
$402$	−655116.	−	1.13469e6i	−0.202187	−	0.350198i
$403$	−503164.	−	871505.i	−0.154329	−	0.267305i
$404$	−2.21819e6	+	3.84202e6i	−0.676153	+	1.17113i
$405$	−144812.			−0.0438699
$406$		0			0
$407$	4.07394e6			1.21907
$408$	−1.15340e6	+	1.99774e6i	−0.343027	+	0.594140i
$409$	−112957.	−	195647.i	−0.0333891	−	0.0578317i	0.848848	−	0.528637i	$-0.177297\pi$
$409$	−112957.	−	195647.i	−0.0333891	−	0.0578317i	−0.882237	+	0.470805i	$0.843963\pi$
$410$	−547236.	−	947841.i	−0.160774	−	0.278468i
$411$	140986.	−	244196.i	0.0411692	−	0.0713072i
$412$	−1.06328e6			−0.308605
$413$		0			0
$414$	710513.			0.203738
$415$	776873.	−	1.34558e6i	0.221426	−	0.383522i
$416$	2.24213e6	+	3.88349e6i	0.635226	+	1.10024i
$417$	−685053.	−	1.18655e6i	−0.192923	−	0.334152i
$418$	−4.42471e6	+	7.66382e6i	−1.23864	+	2.14538i
$419$	−4.31027e6			−1.19941			−0.599707	−	0.800220i	$-0.704716\pi$
$419$	−4.31027e6			−1.19941			−0.599707	+	0.800220i	$0.704716\pi$
$420$		0			0
$421$	1.25088e6			0.343962			0.171981	−	0.985100i	$-0.444983\pi$
$421$	1.25088e6			0.343962			0.171981	+	0.985100i	$0.444983\pi$
$422$	−5.48784e6	+	9.50521e6i	−1.50010	+	2.59825i
$423$	83290.9	+	144264.i	0.0226332	+	0.0392019i
$424$	1.67911e6	+	2.90831e6i	0.453592	+	0.785644i
$425$	1.81424e6	−	3.14236e6i	0.487218	−	0.843887i
$426$	4.80363e6			1.28246
$427$		0			0
$428$	364087.			0.0960719
$429$	−1.49625e6	+	2.59158e6i	−0.392519	+	0.679863i
$430$	−1.99469e6	−	3.45490e6i	−0.520240	−	0.901081i
$431$	2.20397e6	+	3.81738e6i	0.571494	+	0.989857i	0.996413	+	0.0846252i	$0.0269693\pi$
$431$	2.20397e6	+	3.81738e6i	0.571494	+	0.989857i	−0.424919	+	0.905231i	$0.639697\pi$
$432$	13604.8	−	23564.2i	0.00350738	−	0.00607495i
$433$	1.60951e6			0.412549			0.206274	−	0.978494i	$-0.433866\pi$
$433$	1.60951e6			0.412549			0.206274	+	0.978494i	$0.433866\pi$
$434$		0			0
$435$	−1.39752e6			−0.354108
$436$	−2.94555e6	+	5.10184e6i	−0.742079	+	1.28532i
$437$	−1.10493e6	−	1.91380e6i	−0.276779	−	0.479395i
$438$	1.61588e6	+	2.79878e6i	0.402460	+	0.697082i
$439$	−2.21226e6	+	3.83175e6i	−0.547867	+	0.948933i	0.450554	+	0.892749i	$0.351227\pi$
$439$	−2.21226e6	+	3.83175e6i	−0.547867	+	0.948933i	−0.998420	+	0.0561836i	$0.982107\pi$
$440$	1.71379e6			0.422012
$441$		0			0
$442$	1.00771e7			2.45347
$443$	1.80719e6	−	3.13015e6i	0.437517	−	0.757801i	−0.559980	−	0.828506i	$-0.689191\pi$
$443$	1.80719e6	−	3.13015e6i	0.437517	−	0.757801i	0.997497	+	0.0707044i	$0.0225247\pi$
$444$	2.30066e6	+	3.98487e6i	0.553855	+	0.959305i
$445$	−1.59254e6	−	2.75835e6i	−0.381232	−	0.660313i
$446$	−1.36125e6	+	2.35776e6i	−0.324042	+	0.561257i
$447$	−3.26574e6			−0.773060
$448$		0			0
$449$	−467024.			−0.109326			−0.0546630	−	0.998505i	$-0.517408\pi$
$449$	−467024.			−0.109326			−0.0546630	+	0.998505i	$0.517408\pi$
$450$	−980855.	+	1.69889e6i	−0.228336	+	0.395489i
$451$	−1.12531e6	−	1.94910e6i	−0.260515	−	0.451225i
$452$	−2.92865e6	−	5.07257e6i	−0.674251	−	1.16784i
$453$	923065.	−	1.59880e6i	0.211342	−	0.366056i
$454$	2.00285e6			0.456046
$455$		0			0
$456$	−3.87893e6			−0.873575
$457$	300626.	−	520699.i	0.0673342	−	0.116626i	−0.830393	−	0.557178i	$-0.811884\pi$
$457$	300626.	−	520699.i	0.0673342	−	0.116626i	0.897727	+	0.440552i	$0.145217\pi$
$458$	5.64280e6	+	9.77362e6i	1.25699	+	2.17717i
$459$	501388.	+	868430.i	0.111082	+	0.192399i
$460$	−551379.	+	955016.i	−0.121494	+	0.210434i
$461$	−2.87193e6			−0.629392			−0.314696	−	0.949192i	$-0.601903\pi$
$461$	−2.87193e6			−0.629392			−0.314696	+	0.949192i	$0.601903\pi$
$462$		0			0
$463$	−2.91502e6			−0.631959			−0.315979	−	0.948766i	$-0.602333\pi$
$463$	−2.91502e6			−0.631959			−0.315979	+	0.948766i	$0.602333\pi$
$464$	131294.	−	227409.i	0.0283107	−	0.0490357i
$465$	125264.	+	216964.i	0.0268655	+	0.0465324i
$466$	−288953.	−	500481.i	−0.0616399	−	0.106763i
$467$	−3.59688e6	+	6.22998e6i	−0.763192	+	1.32189i	0.178006	+	0.984029i	$0.443035\pi$
$467$	−3.59688e6	+	6.22998e6i	−0.763192	+	1.32189i	−0.941197	+	0.337857i	$0.890298\pi$
$468$	−3.37989e6			−0.713327
$469$		0			0
$470$	−416751.			−0.0870227
$471$	347724.	−	602275.i	0.0722241	−	0.125096i
$472$	−692755.	−	1.19989e6i	−0.143128	−	0.247905i
$473$	−4.10179e6	−	7.10451e6i	−0.842986	−	1.46009i
$474$	−403268.	+	698481.i	−0.0824419	+	0.142794i
$475$	6.10140e6			1.24078
$476$		0			0
$477$	1.45984e6			0.293772
$478$	1.00686e6	−	1.74393e6i	0.201557	−	0.349108i
$479$	−1.39824e6	−	2.42183e6i	−0.278448	−	0.482286i	0.692551	−	0.721369i	$-0.256487\pi$
$479$	−1.39824e6	−	2.42183e6i	−0.278448	−	0.482286i	−0.970999	+	0.239083i	$0.923153\pi$
$480$	−558187.	−	966808.i	−0.110580	−	0.191530i
$481$	3.90040e6	−	6.75569e6i	0.768682	−	1.33140i
$482$	3.98340e6			0.780974
$483$		0			0
$484$	658698.			0.127812
$485$	875456.	−	1.51633e6i	0.168997	−	0.292712i
$486$	−271071.	−	469509.i	−0.0520586	−	0.0901682i
$487$	1.46624e6	+	2.53960e6i	0.280144	+	0.485224i	0.971420	−	0.237367i	$-0.0762843\pi$
$487$	1.46624e6	+	2.53960e6i	0.280144	+	0.485224i	−0.691276	+	0.722591i	$0.742951\pi$
$488$	−325652.	+	564046.i	−0.0619020	+	0.107217i
$489$	−1.66438e6			−0.314761
$490$		0			0
$491$	−3.06121e6			−0.573046			−0.286523	−	0.958073i	$-0.592499\pi$
$491$	−3.06121e6			−0.573046			−0.286523	+	0.958073i	$0.592499\pi$
$492$	1.27099e6	−	2.20142e6i	0.236717	−	0.410006i
$493$	4.83870e6	+	8.38087e6i	0.896626	+	1.55300i
$494$	8.47246e6	+	1.46747e7i	1.56204	+	2.70553i
$495$	372497.	−	645183.i	0.0683297	−	0.118350i
$496$	−47073.4			−0.00859154
$497$		0			0
$498$	5.81687e6			1.05103
$499$	3.27577e6	−	5.67380e6i	0.588928	−	1.02005i	−0.405445	−	0.914119i	$-0.632884\pi$
$499$	3.27577e6	−	5.67380e6i	0.588928	−	1.02005i	0.994373	−	0.105934i	$-0.0337831\pi$
$500$	−3.32583e6	−	5.76052e6i	−0.594943	−	1.03047i
$501$	−581679.	−	1.00750e6i	−0.103535	−	0.179329i
$502$	7.85497e6	−	1.36052e7i	1.39119	−	2.40960i
$503$	1.58524e6			0.279367			0.139684	−	0.990196i	$-0.455391\pi$
$503$	1.58524e6			0.279367			0.139684	+	0.990196i	$0.455391\pi$
$504$		0			0
$505$	−1.87242e6			−0.326719
$506$	−1.82764e6	+	3.16556e6i	−0.317332	+	0.549635i
$507$	1.19421e6	+	2.06843e6i	0.206329	+	0.357373i
$508$	−2.14996e6	−	3.72385e6i	−0.369634	−	0.640225i
$509$	3.38991e6	−	5.87149e6i	0.579953	−	1.00451i	−0.415530	−	0.909579i	$-0.636404\pi$
$509$	3.38991e6	−	5.87149e6i	0.579953	−	1.00451i	0.995484	−	0.0949297i	$-0.0302626\pi$
$510$	−2.50873e6			−0.427099
$511$		0			0
$512$	432315.			0.0728829
$513$	−843098.	+	1.46029e6i	−0.141444	+	0.244988i
$514$	−4.51743e6	−	7.82441e6i	−0.754195	−	1.30630i
$515$	−224383.	−	388643.i	−0.0372796	−	0.0645702i
$516$	4.63279e6	−	8.02422e6i	0.765981	−	1.32672i
$517$	−856990.			−0.141010
$518$		0			0
$519$	−4.57081e6			−0.744859
$520$	1.64078e6	−	2.84192e6i	0.266099	−	0.460897i
$521$	−5.06918e6	−	8.78008e6i	−0.818170	−	1.41711i	−0.907029	−	0.421067i	$-0.861656\pi$
$521$	−5.06918e6	−	8.78008e6i	−0.818170	−	1.41711i	0.0888599	−	0.996044i	$-0.471678\pi$
$522$	−2.61600e6	−	4.53105e6i	−0.420205	−	0.727817i
$523$	49998.6	−	86600.2i	0.00799289	−	0.0138441i	−0.862001	−	0.506906i	$-0.830789\pi$
$523$	49998.6	−	86600.2i	0.00799289	−	0.0138441i	0.869994	+	0.493062i	$0.164122\pi$
$524$	9.19408e6			1.46278
$525$		0			0
$526$	−5.02301e6			−0.791589
$527$	867416.	−	1.50241e6i	0.136051	−	0.235647i
$528$	69990.7	+	121227.i	0.0109259	+	0.0189241i
$529$	2.76178e6	+	4.78354e6i	0.429091	+	0.743207i
$530$	−1.82610e6	+	3.16291e6i	−0.282381	+	0.489099i
$531$	−602290.			−0.0926978
$532$		0			0
$533$	−4.30952e6			−0.657068
$534$	5.96209e6	−	1.03266e7i	0.904785	−	1.56713i
$535$	76833.3	+	133079.i	0.0116055	+	0.0201014i
$536$	1.47729e6	+	2.55873e6i	0.222102	+	0.384692i
$537$	−596651.	+	1.03343e6i	−0.0892862	+	0.154648i
$538$	−5.88620e6			−0.876756
$539$		0			0
$540$	841436.			0.124176
$541$	59871.4	−	103700.i	0.00879481	−	0.0152331i	−0.861595	−	0.507597i	$-0.830534\pi$
$541$	59871.4	−	103700.i	0.00879481	−	0.0152331i	0.870389	+	0.492364i	$0.163867\pi$
$542$	2.51571e6	+	4.35734e6i	0.367843	+	0.637123i
$543$	3.33027e6	+	5.76820e6i	0.484708	+	0.839538i
$544$	−3.86527e6	+	6.69485e6i	−0.559993	+	0.969937i
$545$	−2.48640e6			−0.358574
$546$		0			0
$547$	236568.			0.0338056			0.0169028	−	0.999857i	$-0.494619\pi$
$547$	236568.			0.0338056			0.0169028	+	0.999857i	$0.494619\pi$
$548$	−819209.	+	1.41891e6i	−0.116531	+	0.201838i
$549$	141563.	+	245194.i	0.0200456	+	0.0347200i
$550$	−5.04607e6	−	8.74005e6i	−0.711290	−	1.23199i
$551$	−8.13641e6	+	1.40927e7i	−1.14170	+	1.97749i
$552$	−1.60220e6			−0.223805
$553$		0			0
$554$	−1.53707e7			−2.12774
$555$	−971018.	+	1.68185e6i	−0.133812	+	0.231769i
$556$	3.98054e6	+	6.89449e6i	0.546078	+	0.945834i
$557$	2.41833e6	+	4.18867e6i	0.330277	+	0.572056i	0.982566	−	0.185914i	$-0.0595247\pi$
$557$	2.41833e6	+	4.18867e6i	0.330277	+	0.572056i	−0.652289	+	0.757970i	$0.726191\pi$
$558$	−468961.	+	812264.i	−0.0637604	+	0.110436i
$559$	−1.57083e7			−2.12617
$560$		0			0
$561$	−5.15885e6			−0.692063
$562$	8.31258e6	−	1.43978e7i	1.11018	−	1.92290i
$563$	−2.74147e6	−	4.74837e6i	−0.364513	−	0.631355i	0.624185	−	0.781277i	$-0.285431\pi$
$563$	−2.74147e6	−	4.74837e6i	−0.364513	−	0.631355i	−0.988698	+	0.149922i	$0.952098\pi$
$564$	−483966.	−	838254.i	−0.0640644	−	0.110963i
$565$	1.23607e6	−	2.14093e6i	0.162900	−	0.282151i
$566$	2.30738e7			3.02746
$567$		0			0
$568$	−1.08322e7			−1.40878
$569$	3.48830e6	−	6.04191e6i	0.451682	−	0.782336i	−0.546809	−	0.837258i	$-0.684157\pi$
$569$	3.48830e6	−	6.04191e6i	0.451682	−	0.782336i	0.998491	+	0.0549213i	$0.0174908\pi$
$570$	−2.10925e6	−	3.65333e6i	−0.271920	−	0.470979i
$571$	5.88573e6	+	1.01944e7i	0.755458	+	1.30849i	0.945146	+	0.326647i	$0.105919\pi$
$571$	5.88573e6	+	1.01944e7i	0.755458	+	1.30849i	−0.189689	+	0.981844i	$0.560748\pi$
$572$	8.69404e6	−	1.50585e7i	1.11104	−	1.92439i
$573$	5.24459e6			0.667306
$574$		0			0
$575$	2.52020e6			0.317882
$576$	2.13810e6	−	3.70329e6i	0.268517	−	0.465085i
$577$	3.38646e6	+	5.86552e6i	0.423454	+	0.733444i	0.996275	−	0.0862365i	$-0.0274841\pi$
$577$	3.38646e6	+	5.86552e6i	0.423454	+	0.733444i	−0.572820	+	0.819681i	$0.694151\pi$
$578$	2.16807e6	+	3.75521e6i	0.269932	+	0.467535i
$579$	−1.80407e6	+	3.12474e6i	−0.223644	+	0.387362i
$580$	8.12037e6			1.00232
$581$		0			0
$582$	6.55501e6			0.802169
$583$	−3.75512e6	+	6.50407e6i	−0.457565	+	0.792526i
$584$	−3.64380e6	−	6.31124e6i	−0.442102	−	0.765743i
$585$	−713259.	−	1.23540e6i	−0.0861703	−	0.149251i
$586$	−492242.	+	852588.i	−0.0592154	+	0.102564i
$587$	1.05020e7			1.25799			0.628996	−	0.777408i	$-0.283466\pi$
$587$	1.05020e7			1.25799			0.628996	+	0.777408i	$0.283466\pi$
$588$		0			0
$589$	2.91717e6			0.346476
$590$	753400.	−	1.30493e6i	0.0891036	−	0.154332i
$591$	3.02215e6	+	5.23452e6i	0.355916	+	0.616464i
$592$	−182451.	−	316014.i	−0.0213964	−	0.0370597i
$593$	−3.79537e6	+	6.57378e6i	−0.443218	+	0.767676i	−0.997926	−	0.0643687i	$-0.979497\pi$
$593$	−3.79537e6	+	6.57378e6i	−0.443218	+	0.767676i	0.554708	+	0.832045i	$0.312830\pi$
$594$	2.78909e6			0.324336
$595$		0			0
$596$	1.89758e7			2.18818
$597$	2.04760e6	−	3.54654e6i	0.235130	−	0.407258i
$598$	3.49957e6	+	6.06144e6i	0.400186	+	0.693143i
$599$	6.50992e6	+	1.12755e7i	0.741325	+	1.28401i	0.951892	+	0.306434i	$0.0991358\pi$
$599$	6.50992e6	+	1.12755e7i	0.741325	+	1.28401i	−0.210567	+	0.977580i	$0.567531\pi$
$600$	2.21183e6	−	3.83099e6i	0.250826	−	0.434443i
$601$	−1.41821e7			−1.60160			−0.800801	−	0.598931i	$-0.795592\pi$
$601$	−1.41821e7			−1.60160			−0.800801	+	0.598931i	$0.795592\pi$
$602$		0			0
$603$	1.28437e6			0.143846
$604$	−5.36352e6	+	9.28988e6i	−0.598215	+	1.03614i
$605$	139005.	+	240764.i	0.0154398	+	0.0267426i
$606$	−3.50495e6	−	6.07075e6i	−0.387704	−	0.671523i
$607$	6.03862e6	−	1.04592e7i	0.665221	−	1.15220i	−0.314004	−	0.949422i	$-0.601671\pi$
$607$	6.03862e6	−	1.04592e7i	0.665221	−	1.15220i	0.979225	−	0.202775i	$-0.0649961\pi$
$608$	−1.29991e7			−1.42612
$609$		0			0
$610$	−708320.			−0.0770735
$611$	−820485.	+	1.42112e6i	−0.0889135	+	0.154003i
$612$	−2.91334e6	−	5.04606e6i	−0.314422	−	0.544595i
$613$	1.36265e6	+	2.36018e6i	0.146465	+	0.253684i	0.929918	−	0.367766i	$-0.119877\pi$
$613$	1.36265e6	+	2.36018e6i	0.146465	+	0.253684i	−0.783454	+	0.621450i	$0.786544\pi$
$614$	−6.86855e6	+	1.18967e7i	−0.735266	+	1.27352i
$615$	1.07287e6			0.114382
$616$		0			0
$617$	8.47094e6			0.895816			0.447908	−	0.894080i	$-0.352169\pi$
$617$	8.47094e6			0.895816			0.447908	+	0.894080i	$0.352169\pi$
$618$	840038.	−	1.45499e6i	0.0884765	−	0.153246i
$619$	8.69174e6	+	1.50545e7i	0.911759	+	1.57921i	0.811578	+	0.584243i	$0.198609\pi$
$619$	8.69174e6	+	1.50545e7i	0.911759	+	1.57921i	0.100180	+	0.994969i	$0.468058\pi$
$620$	−727855.	−	1.26068e6i	−0.0760441	−	0.131712i
$621$	−348244.	+	603176.i	−0.0362372	+	0.0627647i
$622$	7.90690e6			0.819464
$623$		0			0
$624$	268037.			0.0275571
$625$	−2.71793e6	+	4.70759e6i	−0.278316	+	0.482058i
$626$	2.31338e6	+	4.00689e6i	0.235945	+	0.408669i
$627$	−4.33737e6	−	7.51255e6i	−0.440613	−	0.763165i
$628$	−2.02047e6	+	3.49955e6i	−0.204434	+	0.354090i
$629$	1.34480e7			1.35529
$630$		0			0
$631$	−6.45149e6			−0.645040			−0.322520	−	0.946563i	$-0.604530\pi$
$631$	−6.45149e6			−0.645040			−0.322520	+	0.946563i	$0.604530\pi$
$632$	909368.	−	1.57507e6i	0.0905622	−	0.156858i
$633$	−5.37951e6	−	9.31759e6i	−0.533622	−	0.924260i
$634$	−2.20353e6	−	3.81663e6i	−0.217719	−	0.377101i
$635$	907413.	−	1.57169e6i	0.0893040	−	0.154679i
$636$	−8.48249e6			−0.831535
$637$		0			0
$638$	2.69164e7			2.61797
$639$	−2.35440e6	+	4.07795e6i	−0.228102	+	0.395084i
$640$	3.36439e6	+	5.82730e6i	0.324681	+	0.562364i
$641$	−8.88581e6	−	1.53907e7i	−0.854185	−	1.47949i	−0.877399	−	0.479761i	$-0.840723\pi$
$641$	−8.88581e6	−	1.53907e7i	−0.854185	−	1.47949i	0.0232142	−	0.999731i	$-0.492610\pi$
$642$	−287647.	+	498218.i	−0.0275437	+	0.0477070i
$643$	9.34806e6			0.891649			0.445825	−	0.895120i	$-0.352910\pi$
$643$	9.34806e6			0.891649			0.445825	+	0.895120i	$0.352910\pi$
$644$		0			0
$645$	3.91063e6			0.370124
$646$	−1.46059e7	+	2.52981e7i	−1.37704	+	2.38510i
$647$	2.67193e6	+	4.62792e6i	0.250937	+	0.434635i	0.963784	−	0.266684i	$-0.0859280\pi$
$647$	2.67193e6	+	4.62792e6i	0.250937	+	0.434635i	−0.712847	+	0.701319i	$0.752595\pi$
$648$	611265.	+	1.05874e6i	0.0571863	+	0.0990495i
$649$	1.54926e6	−	2.68340e6i	0.144382	−	0.250077i
$650$	−1.93245e7			−1.79401
$651$		0			0
$652$	9.67098e6			0.890946
$653$	598506.	−	1.03664e6i	0.0549270	−	0.0951363i	−0.837255	−	0.546813i	$-0.815841\pi$
$653$	598506.	−	1.03664e6i	0.0549270	−	0.0951363i	0.892182	+	0.451677i	$0.149174\pi$
$654$	−4.65425e6	−	8.06140e6i	−0.425506	−	0.736998i
$655$	1.94022e6	+	3.36057e6i	0.176705	+	0.306062i
$656$	−100794.	+	174580.i	−0.00914481	+	0.0158393i
$657$	−3.16796e6			−0.286330
$658$		0			0
$659$	−1.17541e7			−1.05433			−0.527163	−	0.849764i	$-0.676744\pi$
$659$	−1.17541e7			−1.05433			−0.527163	+	0.849764i	$0.676744\pi$
$660$	−2.16441e6	+	3.74887e6i	−0.193410	+	0.334997i
$661$	−9.00573e6	−	1.55984e7i	−0.801706	−	1.38860i	−0.918493	−	0.395438i	$-0.870593\pi$
$661$	−9.00573e6	−	1.55984e7i	−0.801706	−	1.38860i	0.116787	−	0.993157i	$-0.462741\pi$
$662$	−1.00958e7	−	1.74864e7i	−0.895353	−	1.55080i
$663$	−4.93910e6	+	8.55476e6i	−0.436379	+	0.755830i
$664$	−1.31170e7			−1.15456
$665$		0			0
$666$	−7.27054e6			−0.635157
$667$	−3.36076e6	+	5.82102e6i	−0.292498	+	0.506622i
$668$	3.37987e6	+	5.85411e6i	0.293062	+	0.507598i
$669$	−1.33438e6	−	2.31122e6i	−0.115270	−	0.199653i
$670$	−1.60661e6	+	2.78273e6i	−0.138268	+	0.239488i
$671$	−1.45656e6			−0.124888
$672$		0			0
$673$	1.40977e7			1.19981			0.599904	−	0.800072i	$-0.295206\pi$
$673$	1.40977e7			1.19981			0.599904	+	0.800072i	$0.295206\pi$
$674$	−6.23063e6	+	1.07918e7i	−0.528302	+	0.915046i
$675$	−961494.	−	1.66536e6i	−0.0812245	−	0.140685i
$676$	−6.93902e6	−	1.20187e7i	−0.584025	−	1.01156i
$677$	3.82793e6	−	6.63018e6i	0.320991	−	0.555973i	−0.659702	−	0.751527i	$-0.729317\pi$
$677$	3.82793e6	−	6.63018e6i	0.320991	−	0.555973i	0.980693	+	0.195555i	$0.0626507\pi$
$678$	9.25510e6			0.773227
$679$		0			0
$680$	5.65718e6			0.469167
$681$	−981657.	+	1.70028e6i	−0.0811133	+	0.140492i
$682$	−2.41260e6	−	4.17874e6i	−0.198621	−	0.344021i
$683$	5.43378e6	+	9.41158e6i	0.445708	+	0.771988i	0.998101	−	0.0615953i	$-0.0196188\pi$
$683$	5.43378e6	+	9.41158e6i	0.445708	+	0.771988i	−0.552394	+	0.833583i	$0.686285\pi$
$684$	4.89886e6	−	8.48508e6i	0.400364	−	0.693451i
$685$	−691510.			−0.0563083
$686$		0			0
$687$	−1.10628e7			−0.894283
$688$	−367396.	+	636348.i	−0.0295912	+	0.0512535i
$689$	7.19034e6	+	1.24540e7i	0.577034	+	0.999452i
$690$	−871231.	−	1.50902e6i	−0.0696643	−	0.120662i
$691$	−7.30588e6	+	1.26542e7i	−0.582073	+	1.00818i	0.413160	+	0.910658i	$0.364425\pi$
$691$	−7.30588e6	+	1.26542e7i	−0.582073	+	1.00818i	−0.995233	+	0.0975219i	$0.968908\pi$
$692$	2.65589e7			2.10836
$693$		0			0
$694$	−3.48832e7			−2.74927
$695$	−1.68002e6	+	2.90989e6i	−0.131933	+	0.228515i
$696$	5.89907e6	+	1.02175e7i	0.461594	+	0.799505i
$697$	−3.71464e6	−	6.43395e6i	−0.289624	−	0.501644i
$698$	6.04827e6	−	1.04759e7i	0.469886	−	0.813867i
$699$	566498.			0.0438536
$700$		0			0
$701$	1.90104e7			1.46115			0.730577	−	0.682830i	$-0.239251\pi$
$701$	1.90104e7			1.46115			0.730577	+	0.682830i	$0.239251\pi$
$702$	2.67028e6	−	4.62506e6i	0.204510	−	0.354221i
$703$	1.13066e7	+	1.95836e7i	0.862866	+	1.49453i
$704$	1.09996e7	+	1.90518e7i	0.836458	+	1.44879i
$705$	204263.	−	353793.i	0.0154780	−	0.0268088i
$706$	−3.14462e7			−2.37441
$707$		0			0
$708$	3.49964e6			0.262386
$709$	5.79644e6	−	1.00397e7i	0.433058	−	0.750078i	−0.564077	−	0.825722i	$-0.690768\pi$
$709$	5.79644e6	−	1.00397e7i	0.433058	−	0.750078i	0.997135	+	0.0756440i	$0.0241013\pi$
$710$	−5.89021e6	−	1.02021e7i	−0.438516	−	0.759531i
$711$	−395308.	−	684693.i	−0.0293266	−	0.0507951i
$712$	−1.34445e7	+	2.32865e7i	−0.993904	+	1.72149i
$713$	1.20494e6			0.0887653
$714$		0			0
$715$	7.33881e6			0.536859
$716$	3.46687e6	−	6.00479e6i	0.252729	−	0.437739i
$717$	986984.	+	1.70951e6i	0.0716989	+	0.124186i
$718$	6.75205e6	+	1.16949e7i	0.488792	+	0.846613i
$719$	−5.14304e6	+	8.90800e6i	−0.371020	+	0.642626i	−0.989723	−	0.142999i	$-0.954325\pi$
$719$	−5.14304e6	+	8.90800e6i	−0.371020	+	0.642626i	0.618703	+	0.785625i	$0.287659\pi$
$720$	−66728.8			−0.00479713
$721$		0			0
$722$	−2.63868e7			−1.88384
$723$	−1.95239e6	+	3.38163e6i	−0.138906	+	0.240592i
$724$	−1.93507e7	−	3.35164e7i	−1.37199	−	2.37635i
$725$	−9.27900e6	−	1.60717e7i	−0.655626	−	1.13558i
$726$	−520403.	+	901365.i	−0.0366436	+	0.0634686i
$727$	−1.00970e7			−0.708526			−0.354263	−	0.935146i	$-0.615268\pi$
$727$	−1.00970e7			−0.708526			−0.354263	+	0.935146i	$0.615268\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	3.96278e6	−	6.86373e6i	0.275228	−	0.476709i
$731$	−1.35399e7	−	2.34518e7i	−0.937180	−	1.62324i
$732$	−822560.	−	1.42471e6i	−0.0567400	−	0.0982766i
$733$	962010.	−	1.66625e6i	0.0661332	−	0.114546i	−0.831063	−	0.556178i	$-0.812267\pi$
$733$	962010.	−	1.66625e6i	0.0661332	−	0.114546i	0.897196	+	0.441632i	$0.145600\pi$
$734$	−4.57298e7			−3.13299
$735$		0			0
$736$	−5.36932e6			−0.365363
$737$	−3.30376e6	+	5.72228e6i	−0.224047	+	0.388061i
$738$	2.00829e6	+	3.47846e6i	0.135733	+	0.235096i
$739$	−2.10136e6	−	3.63967e6i	−0.141543	−	0.245161i	0.786535	−	0.617546i	$-0.211873\pi$
$739$	−2.10136e6	−	3.63967e6i	−0.141543	−	0.245161i	−0.928078	+	0.372386i	$0.878540\pi$
$740$	5.64215e6	−	9.77249e6i	0.378761	−	0.656034i
$741$	−1.66104e7			−1.11131
$742$		0			0
$743$	−1.99659e7			−1.32684			−0.663418	−	0.748249i	$-0.730895\pi$
$743$	−1.99659e7			−1.32684			−0.663418	+	0.748249i	$0.730895\pi$
$744$	1.05751e6	−	1.83165e6i	0.0700407	−	0.121314i
$745$	4.00445e6	+	6.93592e6i	0.264334	+	0.457839i
$746$	1.81810e7	+	3.14904e7i	1.19611	+	2.07172i
$747$	−2.85102e6	+	4.93812e6i	−0.186939	+	0.323787i
$748$	2.99757e7			1.95892
$749$		0			0
$750$	1.05103e7			0.682277
$751$	1.81988e6	−	3.15212e6i	0.117745	−	0.203940i	−0.801129	−	0.598492i	$-0.795767\pi$
$751$	1.81988e6	−	3.15212e6i	0.117745	−	0.203940i	0.918874	+	0.394552i	$0.129100\pi$
$752$	38380.1	+	66476.4i	0.00247492	+	0.00428670i
$753$	7.69992e6	+	1.33366e7i	0.494878	+	0.857155i
$754$	2.57698e7	−	4.46346e7i	1.65076	−	2.85919i
$755$	−4.52745e6			−0.289059
$756$		0			0
$757$	1.73429e7			1.09997			0.549986	−	0.835174i	$-0.314633\pi$
$757$	1.73429e7			1.09997			0.549986	+	0.835174i	$0.314633\pi$
$758$	−8.04067e6	+	1.39268e7i	−0.508299	+	0.880399i
$759$	−1.79156e6	−	3.10308e6i	−0.112883	−	0.195519i
$760$	4.75635e6	+	8.23824e6i	0.298703	+	0.517369i
$761$	−5.17841e6	+	8.96927e6i	−0.324142	+	0.561430i	−0.981338	−	0.192289i	$-0.938409\pi$
$761$	−5.17841e6	+	8.96927e6i	−0.324142	+	0.561430i	0.657196	+	0.753719i	$0.271742\pi$
$762$	6.79430e6			0.423894
$763$		0			0
$764$	−3.04740e7			−1.88884
$765$	1.22960e6	−	2.12974e6i	0.0759647	−	0.131575i
$766$	−1.44069e7	−	2.49535e7i	−0.887153	−	1.53659i
$767$	−2.96653e6	−	5.13818e6i	−0.182079	−	0.315371i
$768$	−4.99339e6	+	8.64881e6i	−0.305487	+	0.529119i
$769$	1.81548e7			1.10707			0.5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.59061 - 7.95118i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-26.1475 - 45.2888i) q^{4} +(11.0358 - 19.1146i) q^{5} +82.6311 q^{6} -186.333 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.59061 - 7.95118i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-26.1475 - 45.2888i) q^{4} +(11.0358 - 19.1146i) q^{5} +82.6311 q^{6} -186.333 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-101.322 - 175.495i) q^{10} +(-208.355 - 360.881i) q^{11} +(235.327 - 407.599i) q^{12} -797.918 q^{13} +198.644 q^{15} +(-18.6623 + 32.3240i) q^{16} +(-687.775 - 1191.26i) q^{17} +(371.840 + 644.045i) q^{18} +(1156.51 - 2003.14i) q^{19} -1154.23 q^{20} -3825.91 q^{22} +(477.701 - 827.402i) q^{23} +(-838.497 - 1452.32i) q^{24} +(1318.92 + 2284.44i) q^{25} +(-3662.93 + 6344.39i) q^{26} -729.000 q^{27} -7035.29 q^{29} +(911.900 - 1579.46i) q^{30} +(630.596 + 1092.22i) q^{31} +(-2809.98 - 4867.03i) q^{32} +(1875.19 - 3247.93i) q^{33} -12629.2 q^{34} +4235.89 q^{36} +(-4888.22 + 8466.65i) q^{37} +(-10618.2 - 18391.3i) q^{38} +(-3590.63 - 6219.16i) q^{39} +(-2056.33 + 3561.67i) q^{40} +5400.95 q^{41} +19686.6 q^{43} +(-10895.9 + 18872.3i) q^{44} +(893.900 + 1548.28i) q^{45} +(-4385.88 - 7596.57i) q^{46} +(1028.28 - 1781.04i) q^{47} -335.921 q^{48} +24218.7 q^{50} +(6189.98 - 10721.4i) q^{51} +(20863.5 + 36136.7i) q^{52} +(-9011.37 - 15608.2i) q^{53} +(-3346.56 + 5796.41i) q^{54} -9197.45 q^{55} +20817.2 q^{57} +(-32296.3 + 55938.8i) q^{58} +(3717.84 + 6439.49i) q^{59} +(-5194.05 - 8996.36i) q^{60} +(1747.69 - 3027.09i) q^{61} +11579.3 q^{62} -52792.5 q^{64} +(-8805.67 + 15251.9i) q^{65} +(-17216.6 - 29820.0i) q^{66} +(-7928.21 - 13732.1i) q^{67} +(-35967.2 + 62297.0i) q^{68} +8598.62 q^{69} +58133.5 q^{71} +(7546.48 - 13070.9i) q^{72} +(19555.3 + 33870.8i) q^{73} +(44879.9 + 77734.2i) q^{74} +(-11870.3 + 20560.0i) q^{75} -120960. q^{76} -65932.8 q^{78} +(-4880.35 + 8453.01i) q^{79} +(411.906 + 713.442i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(24793.7 - 42943.9i) q^{82} +70395.7 q^{83} -30360.6 q^{85} +(90373.4 - 156531. i) q^{86} +(-31658.8 - 54834.7i) q^{87} +(38823.3 + 67243.9i) q^{88} +(72153.1 - 124973. i) q^{89} +16414.2 q^{90} -49962.7 q^{92} +(-5675.36 + 9830.01i) q^{93} +(-9440.90 - 16352.1i) q^{94} +(-25526.1 - 44212.5i) q^{95} +(25289.8 - 43803.3i) q^{96} +79328.7 q^{97} +33753.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9 + 283 * q^10 - 402 * q^11 + 621 * q^12 - 924 * q^13 - 3273 * q^16 + 276 * q^17 - 243 * q^18 + 510 * q^19 - 9438 * q^20 + 2750 * q^22 - 6900 * q^23 + 1107 * q^24 - 2814 * q^25 - 15138 * q^26 - 5832 * q^27 + 1080 * q^29 - 2547 * q^30 - 6410 * q^31 - 15519 * q^32 + 3618 * q^33 - 42288 * q^34 + 11178 * q^36 - 15250 * q^37 - 41250 * q^38 - 4158 * q^39 - 8547 * q^40 - 8616 * q^41 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 58914 * q^48 - 14604 * q^50 - 2484 * q^51 - 47476 * q^52 - 13692 * q^53 + 2187 * q^54 - 146248 * q^55 + 9180 * q^57 - 52309 * q^58 + 34830 * q^59 - 42471 * q^60 - 5364 * q^61 - 32058 * q^62 - 146974 * q^64 - 66864 * q^65 + 12375 * q^66 + 5994 * q^67 - 58272 * q^68 - 124200 * q^69 + 178536 * q^71 - 9963 * q^72 + 59638 * q^73 + 185442 * q^74 + 25326 * q^75 - 42616 * q^76 - 272484 * q^78 + 44062 * q^79 - 33381 * q^80 - 26244 * q^81 + 57596 * q^82 + 416892 * q^83 + 72648 * q^85 + 136968 * q^86 + 4860 * q^87 - 87597 * q^88 - 77520 * q^89 - 45846 * q^90 + 316512 * q^92 + 57690 * q^93 - 73722 * q^94 + 221376 * q^95 + 139671 * q^96 + 377260 * q^97 + 65124 * q^99

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